The Physics of . . . Changing Lanes

Is traffic passing you by? Relax. You may be moving faster than you think

Donald Redelmeier is riding shotgun in my Chrysler Sebring rental car as I cruise down a four-lane stretch of Bayview Avenue in north Toronto. About 30 feet ahead, a white van slows down to make a left turn. Normally, I wouldn’t think twice about swerving around it. Then again, normally I wouldn’t be sitting beside a scientist who is an expert on the risks of changing lanes. “This is a great lane. Just stay in this lane,” Redelmeier says, in his best driving-instructor’s voice, craning his neck to check the side mirror. “I don’t preach absolute abstinence,” he adds, “but I really resist small temptations.”

Redelmeier, a clinical epidemiologist at the University of Toronto, divides his time between treating accident traumas and figuring out what causes them. Car crashes, he points out, will kill roughly the same number of people worldwide this year as malaria: more than a million. In recent years, he and Stanford statistician Robert Tibshirani have conducted a number of studies on the statistical factors that contribute to this epidemic. They’ve shown that using a cell phone while driving poses the same relative risk as driving with a blood-alcohol level at the legal limit. They’ve demonstrated that drivers are about 35 percent less likely than usual to die in an accident in the month after receiving a traffic ticket, and that driving fatalities increase immediately following the Super Bowl—68 percent in the losing team’s state but only 6 percent in the winning team’s state. Redelmeier has an uncanny knack for using simple statistics to turn up unexpected results. A few years ago he discovered that the average Academy Award winner lives four years longer than other actors and that patients admitted to a hospital over the weekend are 28 percent more likely to die than those admitted on weekdays.

In the late 1990s Redelmeier and Tibshirani began to wonder why it is that drivers change lanes so often, especially in congested traffic. This was no idle concern. Of the 42,643 motor-vehicle-related fatalities in the United States last year, 3 percent—1,304—occurred in cars changing lanes or merging. The scientists theorized that some kind of perceptual illusion was fooling drivers into thinking they were in the slow lane more often than they really were.

To test their hypothesis, Redelmeier and Tibshirani built a computer model that simulated two-lane traffic, then populated it with hundreds of virtual Honda Accords. The cars followed a simple set of rules: They accelerated to catch up with traffic and slowed down if the gap between cars grew too small. What the scientists found confirmed their suspicions: Cars in congested traffic spent more time being overtaken by other cars than they did passing them. Both lanes were moving at the same average speed, but it wouldn’t have seemed that way to the drivers.

Slow cars clump together; fast cars spread out. A driver may pass 10 cars all at once, then move into the slow lane and watch 8 cars speed past one by one. He’ll think he’s moving slower than average, but in fact he’s moving faster. “During any trip, there’ll be far fewer moments of pleasure when you’re passing and far more moments of pain when you’re being overtaken,” Redelmeier says. “That imbalance holds for every driver on the roadway.”

To see if real people fall prey to this same illusion, Redelmeier and Tibshirani mounted a video camera in the backseat of a graduate student’s car and sent him into Toronto’s rush-hour traffic. The student kept his radio tuned to traffic reports. Whenever he heard of some congestion, he hightailed it to the scene and took some footage of cars crawling along in the next lane. Later, Redelmeier and Tibshirani went through the film and selected a four-minute clip in which the driver was moving slightly faster than the cars in the other lane. When they showed it to driving students, 70 percent guessed, incorrectly, that the other lane was moving faster, and 65 percent said they’d try to switch into it.

Other perceptual illusions may also conspire to cause lane envy, Redelmeier and Tibshirani say. People tend to glance at the next lane more often when they’re moving slowly, which can make their situation seem worse than it is. Also, since drivers face forward, the cars they pass disappear quickly behind them while those that overtake them remain annoyingly visible. The simplest solution, Redelmeier jokes, is to gloat a bit more over the cars you’ve passed: “When you’re really getting steamed up in congested traffic, spend a little more time looking into your rearview mirror.”

These findings could apply to other situations in which people have to choose between lanes, as in the grocery store and the bank, Redelmeier says. But highways are where it matters most. “Very few people are dying while in line at the grocery store,” he says.

Mathematicians Bryan Dawson and Troy Riggs of Union University in Jackson, Tennessee, have also studied why drivers tend to feel as if they’re stuck in the slow lane. Their research takes a more statistical tack, however, relying heavily on calculus and probability theory. Dawson and Riggs start by assuming that drivers gauge the speed of traffic by watching the cars that immediately surround them. If you’re driving in the slow lane, you will only rarely pass another car, but you’ll see cars streaming by in the passing lane. “This will give you the misimpression that more people are driving fast and fewer people are driving slow,” Riggs says. In fact, the majority of drivers may be plugging along at your pace while only a few hot rods are in the passing lane.

Riggs and Dawson have developed a mathematical theorem for the phenomenon. It shows that even if a driver can accurately estimate the speed of cars around him, he’s still bound to misjudge the average speed on the highway. Drivers going faster than average will exaggerate how slow other traffic is going; those going slower will exaggerate how fast others are going. Riggs and Dawson calculate, for instance, that if cars are averaging 68 miles per hour on a highway and a driver is going 65 mph, he will estimate that the other cars are going 70 mph—an illusion that’s liable to make him want to change lanes.

That might be the end of the matter, were it not for Nick Bostrom, a postdoctoral fellow in philosophy at Oxford University. In a recent issue of Plus, an online mathematics magazine, Bostrom argued that there’s a more straightforward explanation for lane envy: “If you think about what causes a lane to go slowly, it’s often that there are lots of cars crammed into it. If there are lots of cars, that means on average there will be more drivers and more driver time spent in the slow-moving crammed lanes than in the fast-moving lanes.”

Bostrom compares cars to gas molecules: The way to maximize a road’s overall throughput, he argues, would be to increase the “diffusion rate” to the point where all lanes are in equilibrium. If they could do so safely, he concludes, drivers ought to be changing lanes more rather than less. “Appearances are faithful,” Bostrom says. “More often than not, the next lane is actually faster!”

Redelmeier concedes Bostrom’s point. But he says that research like his and Tibshirani’s shows “just how fallible our judgment is.” Far better to play it safe, he adds. “The risks are always real, but the benefits are sometimes illusory.”